

#include "math.h"
#include "stdint.h"
#include "ahrs.h"

//---------------------------------------------------------------------------------------------------
// Definitions
#define sampleFreq 500.0f // sample frequency in Hz
#define betaDef 0.1f      // 2 * proportional gain

//---------------------------------------------------------------------------------------------------
// Variable definitions
static volatile float beta = betaDef;                             // 2 * proportional gain (Kp)
static volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame

static volatile float gx, gy, gz, ax, ay, az, mx, my, mz;

//this function takes 60.8us.(168M)
void madgwick_ahrs_update(struct ahrs_sensor *sensor, struct attitude *atti)
{
  float recipNorm;
  float s0, s1, s2, s3;
  float qDot1, qDot2, qDot3, qDot4;
  float hx, hy;
  float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;

  gx = sensor->wx;
  gy = sensor->wy;
  gz = sensor->wz;
  ax = sensor->ax;
  ay = sensor->ay;
  az = sensor->az;
  mx = sensor->mx;
  my = sensor->my;
  mz = sensor->mz;

  // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
  if ((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f))
  {
    madgwick_ahrs_updateIMU(sensor, atti);
    return;
  }

  // Rate of change of quaternion from gyroscope
  qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
  qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
  qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
  qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

  // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
  if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f)))
  {

    // Normalise accelerometer measurement
    recipNorm = invSqrt(ax * ax + ay * ay + az * az);
    ax *= recipNorm;
    ay *= recipNorm;
    az *= recipNorm;

    // Normalise magnetometer measurement
    recipNorm = invSqrt(mx * mx + my * my + mz * mz);
    mx *= recipNorm;
    my *= recipNorm;
    mz *= recipNorm;

    // Auxiliary variables to avoid repeated arithmetic
    _2q0mx = 2.0f * q0 * mx;
    _2q0my = 2.0f * q0 * my;
    _2q0mz = 2.0f * q0 * mz;
    _2q1mx = 2.0f * q1 * mx;
    _2q0 = 2.0f * q0;
    _2q1 = 2.0f * q1;
    _2q2 = 2.0f * q2;
    _2q3 = 2.0f * q3;
    _2q0q2 = 2.0f * q0 * q2;
    _2q2q3 = 2.0f * q2 * q3;
    q0q0 = q0 * q0;
    q0q1 = q0 * q1;
    q0q2 = q0 * q2;
    q0q3 = q0 * q3;
    q1q1 = q1 * q1;
    q1q2 = q1 * q2;
    q1q3 = q1 * q3;
    q2q2 = q2 * q2;
    q2q3 = q2 * q3;
    q3q3 = q3 * q3;

    // Reference direction of Earth's magnetic field
    hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
    hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
    _2bx = sqrt(hx * hx + hy * hy);
    _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
    _4bx = 2.0f * _2bx;
    _4bz = 2.0f * _2bz;

    // Gradient decent algorithm corrective step
    s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
    recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
    s0 *= recipNorm;
    s1 *= recipNorm;
    s2 *= recipNorm;
    s3 *= recipNorm;

    // Apply feedback step
    qDot1 -= beta * s0;
    qDot2 -= beta * s1;
    qDot3 -= beta * s2;
    qDot4 -= beta * s3;
  }

  // Integrate rate of change of quaternion to yield quaternion
  q0 += qDot1 * (1.0f / sampleFreq);
  q1 += qDot2 * (1.0f / sampleFreq);
  q2 += qDot3 * (1.0f / sampleFreq);
  q3 += qDot4 * (1.0f / sampleFreq);

  // Normalise quaternion
  recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
  q0 *= recipNorm;
  q1 *= recipNorm;
  q2 *= recipNorm;
  q3 *= recipNorm;

  atti->roll = atan2(2 * q2 * q3 + 2 * q0 * q1, -2 * q1 * q1 - 2 * q2 * q2 + 1) * 57.3; // roll     -pi----pi
  atti->pitch = asin(-2 * q1 * q3 + 2 * q0 * q2) * 57.3;                                // pitch    -pi/2----pi/2
  atti->yaw = atan2(2 * q1 * q2 + 2 * q0 * q3, -2 * q2 * q2 - 2 * q3 * q3 + 1) * 57.3;  // yaw      -pi----pi
}

void madgwick_ahrs_updateIMU(struct ahrs_sensor *sensor, struct attitude *atti)
{
  float recipNorm;
  float s0, s1, s2, s3;
  float qDot1, qDot2, qDot3, qDot4;
  float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2, _8q1, _8q2, q0q0, q1q1, q2q2, q3q3;

  gx = sensor->wx;
  gy = sensor->wy;
  gz = sensor->wz;
  ax = sensor->ax;
  ay = sensor->ay;
  az = sensor->az;
  mx = sensor->mx;
  my = sensor->my;
  mz = sensor->mz;

  // Rate of change of quaternion from gyroscope
  qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
  qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
  qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
  qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);

  // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
  if (!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f)))
  {

    // Normalise accelerometer measurement
    recipNorm = invSqrt(ax * ax + ay * ay + az * az);
    ax *= recipNorm;
    ay *= recipNorm;
    az *= recipNorm;

    // Auxiliary variables to avoid repeated arithmetic
    _2q0 = 2.0f * q0;
    _2q1 = 2.0f * q1;
    _2q2 = 2.0f * q2;
    _2q3 = 2.0f * q3;
    _4q0 = 4.0f * q0;
    _4q1 = 4.0f * q1;
    _4q2 = 4.0f * q2;
    _8q1 = 8.0f * q1;
    _8q2 = 8.0f * q2;
    q0q0 = q0 * q0;
    q1q1 = q1 * q1;
    q2q2 = q2 * q2;
    q3q3 = q3 * q3;

    // Gradient decent algorithm corrective step
    s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
    s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
    s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
    s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
    recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
    s0 *= recipNorm;
    s1 *= recipNorm;
    s2 *= recipNorm;
    s3 *= recipNorm;

    // Apply feedback step
    qDot1 -= beta * s0;
    qDot2 -= beta * s1;
    qDot3 -= beta * s2;
    qDot4 -= beta * s3;
  }

  // Integrate rate of change of quaternion to yield quaternion
  q0 += qDot1 * (1.0f / sampleFreq);
  q1 += qDot2 * (1.0f / sampleFreq);
  q2 += qDot3 * (1.0f / sampleFreq);
  q3 += qDot4 * (1.0f / sampleFreq);

  // Normalise quaternion
  recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
  q0 *= recipNorm;
  q1 *= recipNorm;
  q2 *= recipNorm;
  q3 *= recipNorm;

  atti->roll = atan2(2 * q2 * q3 + 2 * q0 * q1, -2 * q1 * q1 - 2 * q2 * q2 + 1) * 57.3; // roll     -pi----pi
  atti->pitch = asin(-2 * q1 * q3 + 2 * q0 * q2) * 57.3;                                // pitch    -pi/2----pi/2
  atti->yaw = atan2(2 * q1 * q2 + 2 * q0 * q3, -2 * q2 * q2 - 2 * q3 * q3 + 1) * 57.3;  // yaw      -pi----pi
}

/**
  * @brief     Fast inverse square-root, to calculate 1/Sqrt(x)
               sizeof(long) must be 4 bytes.
  * @param[in] input:x
  * @retval    1/Sqrt(x)
  */
float invSqrt(float x)
{
  float halfx = 0.5f * x;
  float y = x;
  long i = *(long *)&y;
  i = 0x5f3759df - (i >> 1);
  y = *(float *)&i;
  y = y * (1.5f - (halfx * y * y));
  return y;
}
